Triangle Perimeter Practice Problems & Solutions

Master triangle perimeter calculations with step-by-step practice problems. Learn formulas for equilateral, isosceles, and scalene triangles with interactive exercises.

📚Practice Calculating Triangle Perimeters
  • Calculate perimeter by adding all three sides of any triangle
  • Apply perimeter formulas for equilateral triangles using one side length
  • Solve isosceles triangle perimeter problems with base and equal sides
  • Work with different units of measurement (mm, cm, meters)
  • Find missing side lengths when perimeter is given
  • Apply triangle perimeter concepts to real-world measurement problems

Understanding Perimeter

Complete explanation with examples

What is the perimeter?

The perimeter indicates the distance we will walk if we start from a certain point, complete a full lap, and return exactly to the starting point.
For example, if we are asked what the perimeter of the waist is, we will take a tape measure and measure the perimeter from a certain point until completing a full lap and returning to the same point from which we started the measurement.
It works exactly the same way in mathematics. The perimeter of any shape is the distance from a specific point back to it after having completely surrounded it.
If this is our figure:

What is the perimeter

Its perimeter will be the distance we cover if we travel along its line from a certain point, and return to it after making a full lap. Imagine that you are surrounding the figure:

Detailed explanation

Practice Perimeter

Test your knowledge with 80 quizzes

666444AAABBBDDDCCC

Calculate the perimeter of the given parallelogram:

Examples with solutions for Perimeter

Step-by-step solutions included
Exercise #1

Calculate the perimeter of the parallelogram ABCD, given that CD is parallel to AB.

777121212AAABBBCCCDDD

Step-by-Step Solution

First we need to remember that pairs of opposite sides in a parallelogram are parallel and equal.

Therefore, AB is parallel to CD and BC is parallel to AD.

From this we can conclude that AB = CD = 7.

Also: BC = AD = 12.

Finally we can calculate the perimeter by adding all the sides together:

7+7+12+12=14+24=38 7+7+12+12=14+24=38

Answer:

38

Video Solution
Exercise #2

Find the perimeter of the triangle ABC

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Step-by-Step Solution

To find the perimeter of triangle △ABC \triangle ABC , we need to sum the lengths of its sides:

  • Side AB=3 AB = 3
  • Side BC=4 BC = 4
  • Side CA=5 CA = 5

Using the formula for the perimeter of a triangle:

Perimeter=AB+BC+CA \text{Perimeter} = AB + BC + CA

Substitute the known values:

Perimeter=3+4+5 \text{Perimeter} = 3 + 4 + 5

Perimeter=12 \text{Perimeter} = 12

Thus, the perimeter of triangle △ABC \triangle ABC is 12\mathbf{12}.

From the multiple-choice options provided, the correct choice is option 1: 12.

Answer:

12

Video Solution
Exercise #3

Calculate the perimeter of the trapezoid according to the following data:

777101010777121212AAABBBCCCDDD

Step-by-Step Solution

To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of all its sides. The steps are as follows:

  • List the lengths of the sides: the bases are 1010 and 1212, and the two non-parallel sides are each 77.
  • Apply the perimeter formula for a trapezoid: P=a+b+c+d P = a + b + c + d .
  • Substitute the given values into the formula: P=10+12+7+7 P = 10 + 12 + 7 + 7 .
  • Calculate the sum: P=10+12+7+7=36 P = 10 + 12 + 7 + 7 = 36 .

Therefore, the perimeter of the trapezoid is 36 36 .

This matches the correct answer choice from the provided options.

Answer:

36

Video Solution
Exercise #4

Calculate the perimeter of the trapezoid below:

101010111111555101010

Step-by-Step Solution

To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of its sides:

  • Step 1: Identify the side lengths of the trapezoid:
    Top side =10 = 10 , Bottom side =5 = 5 , Left side =10 = 10 , Right side =11 = 11 .
  • Step 2: Apply the perimeter formula:
    The formula for the perimeter P P of a trapezoid is P=a+b+c+d P = a + b + c + d .
  • Step 3: Perform the calculations:
    Substitute the given lengths into the formula:
    P=10+5+10+11=36 P = 10 + 5 + 10 + 11 = 36 .

Therefore, the perimeter of the trapezoid is 36 36 .

Answer:

36

Exercise #5

Calculate the perimeter of the trapezoid below:

161616161616111151515

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Identify the given side lengths of the trapezoid.
  • Apply the formula for the perimeter of a trapezoid.
  • Perform the addition of all side lengths to calculate the perimeter.

Let's work through each step:

Step 1: Identify the given side lengths. The trapezoid has:

  • Top base: a=16 a = 16
  • Bottom base: b=1 b = 1
  • Non-parallel side: c=15 c = 15
  • Other non-parallel side: d=16 d = 16

Step 2: We'll use the formula for the perimeter of a trapezoid:

P=a+b+c+d P = a + b + c + d

Step 3: Plug in the values and perform the calculation:

P=16+1+15+16 P = 16 + 1 + 15 + 16

P=48 P = 48

Therefore, the perimeter of the trapezoid is 48 48 .

Answer:

48

Frequently Asked Questions

Everything you need to know about Perimeter

What is the formula for finding the perimeter of a triangle?

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The perimeter of a triangle is found by adding all three sides together: P = a + b + c, where a, b, and c are the lengths of the three sides. This formula works for all types of triangles including scalene, isosceles, and equilateral triangles.

How do you find the perimeter of an equilateral triangle?

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For an equilateral triangle, all three sides are equal in length. The formula is P = 3a, where 'a' is the length of one side. Simply multiply the side length by 3 to get the perimeter.

What information do I need to find an isosceles triangle's perimeter?

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For an isosceles triangle, you need the length of the base and the length of one of the two equal sides. The formula is P = base + 2(equal side), since two sides have the same measurement.

Can triangle perimeter be measured in different units?

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Yes, triangle perimeter can be measured in various units including: • Millimeters (mm) • Centimeters (cm) • Meters (m) • Inches or feet Remember to convert units when necessary: 1 cm = 10 mm, 1 meter = 100 cm.

How do I solve triangle perimeter word problems?

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Follow these steps: 1) Identify what type of triangle you have, 2) Write down the known side lengths, 3) Apply the appropriate perimeter formula, 4) Add the measurements carefully, 5) Include the correct units in your final answer.

What's the difference between perimeter and area of a triangle?

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Perimeter measures the distance around the outside of a triangle by adding all three sides together. Area measures the space inside the triangle using the formula A = ½ × base × height. Perimeter is measured in linear units (cm, m) while area uses square units (cm², m²).

Can I find a missing side if I know the triangle's perimeter?

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Yes, if you know the perimeter and two side lengths, you can find the third side using: missing side = perimeter - (side 1 + side 2). This works because the perimeter equals the sum of all three sides.

What are common mistakes when calculating triangle perimeter?

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Common errors include: forgetting to add all three sides, mixing up different units of measurement, confusing perimeter with area formulas, and making arithmetic mistakes when adding the side lengths. Always double-check your addition and units.

More Perimeter Questions

Click on any question to see the complete solution with step-by-step explanations

Perimeter of a Rectangle

Calculate Rectangle Perimeter: Finding the Total Length of a 4.8 cm × 12 cm Rectangle Calculate the Perimeter: Finding Border Length in a 2×4×5 Rectangular Diagram Calculate Parallelogram Area: Rectangle with Perimeter 24 Inside Calculate the Perimeter: Rectangle Composed of Two Equal Squares Calculate Rectangle Area: Given Perimeter 30cm and Height 5cm

Circumference

Calculate Circle Radius Given Circumference C=81: Geometric Problem Calculate Circle Radius When Circumference = 9: Using C = 2πr Calculate Circle Radius: Finding r When C=35.6 Calculate Radius from Circumference: Finding r When C = 400 Calculate Circle Radius: Using Given Circumference Measurement

Perimeter of a Parallelogram

Calculate Parallelogram Area: 38cm Perimeter with Proportional Sides Calculate Parallelogram Height: Area 24 cm², Perimeter 24 cm with Double-Length Side Calculate Parallelogram Area: 22cm Perimeter with 2cm Height Calculate Parallelogram Area: 22cm Perimeter with 3cm Height Parallelogram Side Length: Finding Missing Side Given 9cm and 30cm Perimeter

Perimeter of a Trapezoid

Calculate Trapezoid Perimeter: Inside an Isosceles Triangle with Height 8 Calculate Trapezoid Perimeters: Comparing Two Shapes with 7-Unit Parallel Sides Calculate Trapezoid Perimeter: Finding the Sum of Sides 4, 5, 6, and 9 Calculate Trapezoid Perimeter: Finding Total Length of 7.5, 4, 1.5, and 3 Units Calculate Trapezoid Perimeter: Finding the Sum of 2.5, 10.4, 5.3, and 6 Units

Perimeter of a Triangle

Calculate Triangle Perimeter: Finding the Sum of Sides 6, 8, and 10 Calculate Triangle Perimeter: Finding the Sum of Sides 7, 11, and 13 Calculate the Perimeter of an Equilateral Triangle with 5-Unit Sides Find X in an Equilateral Triangle with 33cm Perimeter Calculate the Perimeter: Isosceles Triangle with Sides 6 and Base 4

Continue Your Math Journey

Master Perimeter first, then advance to these related topics that build on your fraction skills

Suggested Topics to Practice in Advance

AreaThe sides or edges of a triangleTriangle HeightThe Sum of the Interior Angles of a TriangleExterior angles of a triangleTypes of TrianglesObtuse TriangleEquilateral triangleIdentification of an Isosceles TriangleScalene triangleAcute triangleIsosceles triangleThe Area of a TriangleArea of a right triangleArea of Isosceles TrianglesArea of a Scalene TriangleArea of Equilateral TrianglesAreas of Polygons for 7th GradeRight TriangleMedian in a triangleCenter of a Triangle - The Centroid - The Intersection Point of MediansHow do we calculate the area of complex shapes?How to calculate the area of a triangle using trigonometry?All terms in triangle calculation

Topics Learned in Later Sections

TrianglePerimeter of a triangleHow do we calculate the perimeter of polygons?

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems
Applying the formula Applying the formula Applying the formula Applying the formula Applying the formula A shape consisting of several shapes (requiring the same formula) Calculate The Missing Side based on the formula Calculate The Missing Side based on the formula Calculate The Missing Side based on the formula Calculating parts of the circle Comparison between 2 of the same shape with an identical perimeter Comprehension exercises Finding Area based off Perimeter and Vice Versa Finding Area based off Perimeter and Vice Versa Finding Area based off Perimeter and Vice Versa Finding Area based off Perimeter and Vice Versa Finding Area based off Perimeter and Vice Versa Identifying and defining elements Identify the greater value Increasing a specific element by addition of.....or multiplication by....... Subtraction or addition to a larger shape Using additional geometric shapes Using additional geometric shapes Using congruence and similarity Using Pythagoras' theorem Using Pythagoras' theorem Using Pythagoras' theorem Using the properties of the perimeter of the parallelogram Using variables Using variables Using variables Using variables Verifying whether or not the formula is applicable Worded problems